Question

A ladder leaning against a wall creates a slope of 8/3
. Using the inverse of tangent, what is the angle formed where the ladder rests on the wall?(1 point)
Responses

67.9°
67.9 degrees

20.6°
20.6 degrees

69.4°
69.4 degrees

22.1°
22.1 degrees

Answer 1

To find the angle formed where the ladder rests on the wall, you can use the inverse tangent (arctan) function.

Given the slope \( \frac{8}{3} \), we can interpret this as:
- Opposite side = 8 (height where the ladder touches the wall)
- Adjacent side = 3 (base of the triangle formed by the ladder, wall, and ground)

To find the angle \( \theta \) formed where the ladder rests on the wall:

\[
\theta = \arctan\left(\frac{8}{3}\right)
\]

Now, let's calculate it:

Using a calculator:

\[
\theta \approx \arctan(2.6667) \approx 69.4^\circ
\]

So, the angle at which the ladder rests against the wall is approximately **69.4°**.

Therefore, the correct response is:

**69.4°**